Stephen Montgomery-Smith, Finite time blow up for a Navier-Stokes like equation. Proc. A.M.S., 129, (2001), 3017-3023. We consider an equation similar to the Navier-Stokes equation. We show that there is initial data that exists in every Triebel-Lizorkin or Besov space (and hence in every Lebesgue and Sobolev space), such that after a finite time, the solution is in no Triebel-Lizorkin or Besov space (and hence in no Lebesgue or Sobolev space). The purpose is to show the limitations of the so called semigroup method for the Navier-Stokes equation. We also consider the possibility of existence of solutions with initial data in the Besov space \(B_\infty^{-1,\infty}\). We give initial data in this space for which there is no reasonable solution for the Navier-Stokes like equation. (tex, dvi, ps, pdf, html.)


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